Atypical Kawasaki Disease Presentation in a Previously Healthy Infant: A Diagnostic Challenge.

Kawasaki disease (KD) is an acute systemic vasculitis primarily affecting children, characterized by fever and multisystem involvement. We present a compelling case of KD in a previously healthy 13-week-old infant who presented with fever, irritability, reduced feeding, and the subsequent development of classical mucocutaneous manifestations, including bilateral non-purulent conjunctivitis, cracked lips, and an erythematous rash. Laboratory findings revealed elevated inflammatory markers, thrombocytosis, and neutrophilic leukocytosis, consistent with the diagnosis. The patient was started on intravenous immunoglobulins (IVIG) at a dose of 2g/kg, IV methylprednisolone, and a high dose of aspirin. The infant was eventually transferred to a tertiary care hospital for comprehensive management. The case is intriguing due to its presentation in an atypical age group. Prompt recognition and management of KD are crucial to prevent the development of coronary artery abnormalities. This case underscores the importance of considering KD in the differential diagnosis of infants with fever and unusual clinical presentations, even in the absence of typical cardiac involvement. Early identification and appropriate treatment are essential to prevent potential complications and improve outcomes.

Characteristic polynomials, spectral-based Riemann-Zeta functions and entropy indices of n-dimensional hypercubes.

Abstract: We obtain the characteristic polynomials and a number of spectral-based indices such as the Riemann-Zeta functional indices and spectral entropies of n-dimensional hypercubes using recursive Hadamard transforms. The computed numerical results are constructed for up to 23-dimensional hypercubes. While the graph energies exhibit a J-curve as a function of the dimension of the n-cubes, the spectra-based entropies exhibit a linear dependence on the dimension. We have also provided structural interpretations for the coefficients of the characteristic polynomials of n-cubes and obtain expressions for the integer sequences formed by the spectral-based Riemann-Zeta functions.

Topological Entropy Characterization, NMR and ESR Spectral Patterns of Coronene-Based Transition Metal Organic Frameworks.

Metal organic frameworks (MOFs) are topical crystalline materials with high porosity and inner surface areas synthesized from naturally occurring minerals. Such MOFs with transition metals have attracted considerable attention because of their fascinating morphological diversity and tunable characteristics. The coronene-based structural frameworks with transition metal atoms are synthesized by repeating a fixed coronene unit at several levels. In this study, topological indices and NMR and ESR spectral patterns are computed for these MOFs to shed light on their structures and spectral properties. We obtained mathematical expressions of topological indices based on degree and degree-sum values of MOFs for the rectangular, hexagonal, and parallelogram peripheral shapes. Furthermore, the entropy measures of these novel frameworks are evaluated with the help of index functionals and compared to a wide range of degree-based descriptors. The NMR and ESR spectral patterns have been obtained from the distance degree vector sequences and symmetries for the three MOFs.

Nanoporous and nano thickness film-forming bioactive composition for biomedical applications.

Unmanageable bleeding is one of the significant causes of mortality. Attaining rapid hemostasis ensures subject survivability as a first aid during combats, road accidents, surgeries that reduce mortality. Nanoporous fibers reinforced composite scaffold (NFRCS) developed by a simple hemostatic film-forming composition (HFFC) (as a continuous phase) can trigger and intensify hemostasis. NFRCS developed was based on the dragonfly wing structure's structural design. Dragonfly wing structure consists of cross-veins and longitudinal wing veins inter-connected with wing membrane to maintain the microstructural integrity. The HFFC uniformly surface coats the fibers with nano thickness film and interconnects the randomly distributed cotton gauge (Ct) (dispersed phase), resulting in the formation of a nanoporous structure. Integrating continuous and dispersed phases reduce the product cost by ten times that of marketed products. The modified NFRCS (tampon or wrist band) can be used for various biomedical applications. The in vivo studies conclude that the developed Cp NFRCS triggers and intensifies the coagulation process at the application site. The NFRCS could regulate the microenvironment and act at the cellular level due to its nanoporous structure, which resulted in better wound healing in the excision wound model.

Topological and Spectral Properties of Wavy Zigzag Nanoribbons.

Low-dimensional graphene-based nanomaterials are interesting due to their cutting-edge electronic and magnetic properties. Their large surface area, strong mechanical resistance, and electronic properties have enabled potential pharmaceutical and opto-electronic applications. Graphene nanoribbons (GNRs) are graphene strips of nanometer size possessing zigzag and armchair edge geometries with tunable widths. Despite the recent developments in the characterization, design and synthesis of GNRs, the study of electronic, magnetic and topological properties, GNRs continue to pose a challenge owing to their multidimensionality. In this study, we obtain the topological and electronic properties of a series of wave-like nanoribbons comprising nanographene units with zigzag-shaped edges. The edge partition techniques based on the convex components are employed to compute the mathematical formulae of molecular descriptors for the wave-like zigzag GNRs. We have also obtained the spectral and energetic properties including HOMO-LUMO gaps, bond delocalization energies, resonance energies, 13C NMR and ESR patterns for the GNRs. All of these computations reveal zero to very low HOMO-LUMO gaps that make these nanoribbons potential candidates for topological spintronics.

Topological Characterization and Graph Entropies of Tessellations of Kekulene Structures: Existence of Isentropic Structures and Applications to Thermochemistry, Nuclear Magnetic Resonance, and Electron Spin Resonance.

Tessellations of kekulenes and cycloarenes are of considerable interest as nanomolecular belts in trapping and transportation of heavy metal ions and chloride ions, as they possess optimal electronic features and pore sizes. A class of cycloarenes called kekulenes have been the focus of several experimental and theoretical studies from the stand point of aromaticity, superaromaticity, chirality, and novel electrical and magnetic properties. In the present study, we investigate the entropies and topological characterization of different tessellations of kekulenes through topological computations of superaromatic structures with pores. We introduce the self-powered vertex degree-based topological indices and then derive the graph entropy measures for three different tessellations (zigzag, armchair, and rectangular) via various molecular descriptors that we derive here. Several applications to computing the molecular properties are pointed out. We demonstrate the existence of isentropic and yet nonisomorphic tessellations of kekulenes for the first time. The two tessellations are predicted to be quite close in energy with comparable energy gaps. Graph theory-based PPP methods with parameters derived from higher levels of theory are proposed to be promising tools for the predictions of relative stabilities of kekulene tessellations. We show that the developed techniques can be applied in the general context of artificial intelligence for the machine generation of nuclear magnetic resonance and electron spin resonance spectroscopic patterns as well as in robust computations of thermochemistry of a large combinatorial libraries of tessellations of kekulenes through the generation of bond-equivalence classes.

Biochemical and phylogenetic networks-II: X-trees and phylogenetic trees.

The present study, which is a continuation of the previous paper, augments a recent work on the use of phylogenetic networks. We develop techniques to characterize the topology of various X-trees and binary trees of biological and phylogenetic interests. We have obtained the results for various k-level X-trees and phylogenetic networks with variants of Zagreb, Szeged, Padmakar-Ivan, Schultz and Atom Bond Connectivity topological indices.

Beam forming of shear horizontal guided waves by multi-row staggered magnet configurations.

This paper introduces the wave interferences effects of staggering multiple rows of Periodically Permanent Magnets (PPM) in an Electromagnetic Acoustic Transducer (EMAT) configuration to achieve selective beam forming effects such as steering, focusing and de-focusing of guided ultrasonic waves. The shear horizontal (SH) guided ultrasonic wave in a metal plate was used to demonstrate these effects using numerical Finite Element Model (FEM) that were validated using experiments.

Biochemical and phylogenetic networks-I: hypertrees and corona products.

We have obtained graph-theoretically based topological indices for the characterization of certain graph theoretical networks of biochemical interest. We have derived certain distance, degree and eccentricity based topological indices for various k-level hypertrees and corona product of hypertrees. We have also pointed out errors in a previous study. The validity of our results is supported by computer codes for the respective indices. Several biochemical applications are pointed out.

An Overview of Ovarian Cancer: Molecular Processes Involved and Development of Target-based Chemotherapeutics.

Ovarian cancer is one of the leading gynecologic diseases with a high mortality rate worldwide. Current statistical studies on cancer reveal that over the past two decades, the fifth most common cause of death related to cancer in females of the western world is ovarian cancer. In spite of significant strides made in genomics, proteomics and radiomics, there has been little progress in transitioning these research advances into effective clinical administration of ovarian cancer. Consequently, researchers have diverted their attention to finding various molecular processes involved in the development of this cancer and how these processes can be exploited to develop potential chemotherapeutics to treat this cancer. The present review gives an overview of these studies which may update the researchers on where we stand and where to go further. The unfortunate situation with ovarian cancer that still exists is that most patients with it do not show any symptoms until the disease has moved to an advanced stage. Undoubtedly, several targets-based drugs have been developed to treat it, but drug-resistance and the recurrence of this disease are still a problem. For the development of potential chemotherapeutics for ovarian cancer, however, some theoretical approaches have also been applied. A description of such methods and their success in this direction is also covered in this review.

Combinatorics of Supergiant Fullerenes: Enumeration of Polysubstituted Isomers, Chirality, Nuclear Magnetic Resonance, Electron Spin Resonance Patterns, and Vibrational Modes from C70 to C150000.

We have developed combinatorial techniques for the enumeration of isomers of polysubstituted giant fullerenes through icosahedral C150000 and applied the techniques to chirality of the isomers, NMR spectroscopy, and group theoretical analysis of the vibrational modes of supergiant fullerenes. We have employed a combination of distance-degree vectorial sequences, self-returning walk sequences followed by our generalization of Sheehan's version of Pólya's theorem, and Möbius inversion technique extended to all irreducible representations of the point groups of giant fullerenes. The concept of shell equivalence classes was utilized to analyze supergiant fullerenes. We have applied these techniques to golden fullerenes in the series C60m2 for m of up to 50 or C150000 as well as giant fullerenes in the series C180m2 and C70(D5h). We have employed computational and combinatorial tools to enumerate both chiral and achiral isomers of substituted and hetero giant fullerenes as well as NMR-generating functions for the giant fullerenes. The techniques also provide efficient tools to enumerate all of the vibrational modes of giant fullerenes in terms of the shell partitions. General combinatorial formulae are obtained for larger polysubstituted golden fullerenes of the series C60m2 for any m, and thus the techniques are applied to larger fullerenes such as C150000. New insights into chirality measures, NMR, ESR hyperfine structures, and vibrational modes of supergiant fullerenes are provided using the novel combinatorial techniques.

Nonrigid water octamer: Computations with the 8-cube.

A 8-cube model of the fully nonrigid water octamer is considered within the 8-dimensional hyperoctahedral wreath product group with 10,321,920 operations and 185 irreducible representations by employing computational and mathematical techniques. For the two lowest-lying isomers of (H2 O)8 with D2d and S4 symmetries of a rigid (H2 O)8 , correlation tables and nuclear spin statistics are constructed for the tunneling splittings of the rotational levels are computed by a computational matrix polynomial generating function technique combined with Möbius inversion, and the relationship to the 8-cube multinomials are pointed out. Multinomial generating functions combined with the induced representation techniques are employed to compute and construct the nuclear spin species, nuclear spin statistical weights and tunneling splittings of rovibronic levels. We have also computed the spin statistical weights and tunneling splittings of the rotational levels for a semirigid water octamer within the wreath product Oh [S2 ] consisting of 12,288 operations.

Computations of Colorings 7D-Hypercube's Hyperplanes for All Irreducible Representations.

In the present study, we compute and enumerate the colorings of 7D-hypercube for all of its hyperplanes (q = 1-7) for all 110 irreducible representations (IRs) of the seventh-dimensional hyperoctahedral group consisting of 645,120 symmetry operations. The computations of colorings of the 7D-hypercube are motivated by a number of chemical and biological applications such as the 7D-hypercube representation of the periodic table, hypercube representations of water heptamer clusters, genetic regulatory networks, isomerization graphs, massively large data representations, and so forth. We have employed the Möbius inversion technique combined with generalized character cycle indices for 110 IRs to compute the generating functions for colorings of seven different types of hyperplanes of the 7D-hypercube varying from the vertices (q = 7) to hexeracts (q = 1) of the 7D-hypercube. Explicit computed tables are provided for 110 IRs from q = 1 to q = 7 for the 7D-hypercube. © 2019 Wiley Periodicals, Inc.

Edge Distance-based Topological Indices of Strength-weighted Graphs and their Application to Coronoid Systems, Carbon Nanocones and SiO2 Nanostructures.

The edge-Wiener index is conceived in analogous to the traditional Wiener index and it is defined as the sum of distances between all pairs of edges of a graph G. In the recent years, it has received considerable attention for determining the variations of its computation. Motivated by the method of computation of the traditional Wiener index based on canonical metric representation, we present the techniques to compute the edge-Wiener and vertex-edge-Wiener indices of G by dissecting the original graph G into smaller strength-weighted quotient graphs with respect to Djokovic-Winkler relation. These techniques have been applied to compute the exact analytic expressions for the edge-Wiener and vertex-edge-Wiener indices of coronoid systems, carbon nanocones and SiO2 nanostructures. In addition, we have reduced these techniques to the subdivision of partial cubes and applied to the circumcoronene series of benzenoid systems.

Quantum Molecular Dynamics, Topological, Group Theoretical and Graph Theoretical Studies of Protein-Protein Interactions.

BACKGROUND: Protein-protein interactions (PPIs) are becoming increasingly important as PPIs form the basis of multiple aggregation-related diseases such as cancer, Creutzfeldt-Jakob, and Alzheimer's diseases. This mini-review presents hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies facilitate the discovery of some PPI inhibitors of therapeutic importance. OBJECTIVE: The objective of this review is to present hybrid quantum molecular dynamics, quantum chemical, topological, group theoretical, graph theoretical, and docking studies of PPIs. We also show how these theoretical studies enable the discovery of some PPI inhibitors of therapeutic importance. METHODS: This article presents a detailed survey of hybrid quantum dynamics that combines classical and quantum MD for PPIs. The article also surveys various developments pertinent to topological, graph theoretical, group theoretical and docking studies of PPIs and highlight how the methods facilitate the discovery of some PPI inhibitors of therapeutic importance. RESULTS: It is shown that it is important to include higher-level quantum chemical computations for accurate computations of free energies and electrostatics of PPIs and Drugs with PPIs, and thus techniques that combine classical MD tools with quantum MD are preferred choices. Topological, graph theoretical and group theoretical techniques are shown to be important in studying large network of PPIs comprised of over 100,000 proteins where quantum chemical and other techniques are not feasible. Hence, multiple techniques are needed for PPIs. CONCLUSION: Drug discovery and our understanding of complex PPIs require multifaceted techniques that involve several disciplines such as quantum chemistry, topology, graph theory, knot theory and group theory, thus demonstrating a compelling need for a multi-disciplinary approach to the problem.

Combinatorial Enumeration of Isomers of Superaromatic Polysubstituted Cycloarenes and Coronoid Hydrocarbons with Applications to NMR.

We have employed combinatorial techniques based on character cycle indices, Pólya's theory, and Euler totem function to enumerate isomers of polysubstituted cycloarenes and coronoid hydrocarbons which have been receiving considerable attention because of their superaromaticity, ring currents, and interesting magnetic properties. Systematic enumeration and construction of tables of polysubstituted isomers such as fluoro-chloro superaromatic hydrocarbons are considered as they are of interest in the study of environmental pollutants and toxicity. Isomers of fluoro-chloro polysubstituted donut shaped circumkekulenes, circumseptulenes, circumoctulenes, etc., are enumerated in addition to other cycloarenes, polycyclic circumcoronaphenes and coronoids. Applications to 13C NMR, proton NMR and multiple quantum NMR spectroscopies of these superaromatic species are considered.

Quantum molecular modeling of hepatitis C virus inhibition through non-structural protein 5B polymerase receptor binding of C5-arylidene rhodanines.

We have carried out high-level quantum chemical computations followed by molecular docking studies on a set of 17C5-arylidene rhodanine isomers to provide insights into the binding modes with different reported binding pockets of the nonstructural protein 5B (NS5B) polymerase that contribute to the hepatitis C virus (HCV) inhibition. We optimized the multi-target profile of the selected rhodanine analogs to investigate potential non-nucleotide inhibitors (NNIs) by quantum chemical optimization of the 18 isomers followed by docking with quantum chemically optimized structures of each isomer with NS5B polymerase at multiple binding pockets. The binding affinities of the PP-I, PP-II and TP-II pockets of NS5B polymerase were analyzed for all the 17 isomers of 2-[(5Z)-5-(2,4-dichlorobenzylidene)-4-oxo-2-thioxo-1,3-thiazolidin-3-yl]-3-phenylpropanoic acid. On the basis of binding propensity at the different pockets and inhibitor constants, we ranked these isomers as potential candidates for the HCV inhibition. We have identified four isomers as promising NNIs of NS5B polymerase with comparable binding and inhibition to the standard (1,3) dichloro substituted isomer that exhibits in vitro activity and several other isomers as candidates in a "multi-targeted drug" approach.

Mathematical and Computational Techniques for Drug Discovery: Promises and Developments.

We review various mathematical and computational techniques for drug discovery exemplifying some recent works pertinent to group theory of nested structures of relevance to phylogeny, topological, computational and combinatorial methods for drug discovery for multiple viral infections. We have reviewed techniques from topology, combinatorics, graph theory and knot theory that facilitate topological and mathematical characterizations of protein-protein interactions, molecular-target interactions, proteomics, genomics and statistical data reduction procedures for a large set of starting chemicals in drug discovery. We have provided an overview of group theoretical techniques pertinent to phylogeny, protein dynamics especially in intrinsically disordered proteins, DNA base permutations and related algorithms. We consider computational techniques derived from high level quantum chemical computations such as QM/MM ONIOM methods, quantum chemical optimization of geometries complexes, and molecular dynamics methods for providing insights into protein-drug interactions. We have considered complexes pertinent to Hepatitis Virus C non-structural protein 5B polymerase receptor binding of C5-Arylidebne rhodanines, complexes of synthetic potential vaccine molecules with dengue virus (DENV) and HIV-1 virus as examples of various simulation studies that exemplify the utility of computational tools. It is demonstrated that these combinatorial and computational techniques in conjunction with experiments can provide promising new insights into drug discovery. These techniques also demonstrate the need to consider a new multiple site or allosteric binding approach to drug discovery, as these studies reveal the existence of multiple binding sites.

Quantum Chemical and Docking Insights into Bioavailability Enhancement of Curcumin by Piperine in Pepper.

We combine quantum chemical and molecular docking techniques to provide new insights into how piperine molecule in various forms of pepper enhances bioavailability of a number of drugs including curcumin in turmeric for which it increases its bioavailability by a 20-fold. We have carried out docking studies of quantum chemically optimized piperine structure binding to curcumin, CYP3A4 in cytochrome P450, p-Glycoprotein and UDP-glucuronosyltransferase (UGT), the enzyme responsible for glucuronosylation, which increases the solubility of curcumin. All of these studies establish that piperine binds to multiple sites on the enzymes and also intercalates with curcumin forming a hydrogen bonded complex with curcumin. The conjugated network of double bonds and the presence of multiple charge centers of piperine offer optimal binding sites for piperine to bind to enzymes such as UDP-GDH, UGT, and CYP3A4. Piperine competes for curcumin's intermolecular hydrogen bonding and its stacking propensity by hydrogen bonding with enolic proton of curcumin. This facilitates its metabolic transport, thereby increasing its bioavailability both through intercalation into curcumin layers through intermolecular hydrogen bonding, and by inhibiting enzymes that cause glucuronosylation of curcumin.